Existence of Longitudinal Waves
Clifford Ambrose Truesdell · The Journal of the Acoustical Society of America · 1966
Hadamard [Leçons sur la propagation des ondes (Hermann Cie., Paris, 1903)] showed that, at a point of a strained elastic body where the elasticity operator is strongly elliptic, the squared wavespeed corresponding to any possible real amplitude is positive. Under the same conditions, we see that at the same point there exists at least one direction in which a longitudinal discontinuity may propagate. Taken together, these two theorems guarantee the compatibility of some real, propagating longitudinal wave.